Muzak to math by

We are in the throes of initial planning for a series of “Music and Maths” sessions aimed at 16-19 year old students, to culminate in a public performance. Using a mix of computing technologies and Blue Peter style building from scratch, the idea is to start from rediscovery of the twelve note scale and build up through construction of instruments.

The first problem we have encountered is an apparent dearth of devices or software which will listen to a note and read out its frequency. There are plenty of them (aimed at instrument tuning) which will do it the other way round, reading out a note name (C, F#, G, etc), but not a frequency. And although we did work out an alternative approach based on these guitar tuners, the interference from a building full of computing equipment, hearing aid loop generators, WiFi networks, several hundred cellphones etc, swamped them and made them useless.

A microphone attached to an oscilloscope is too unwieldy for our purpose: first introduce the oscilloscope, then explain the setting of time bases, learn to disregard noise … a one hour session would be over before anything useful had even stared. It will be useful and interesting further in, but not at the beginning.

Plan C involves auditory comparison of a tone generator signal to played keyboard and guitar string notes, by tweaking the frequency specified in the generator and deciding by consensus when a played note has been matched. This looks initially promising. We have started with NCH’s tone generator, which works well; the synthesiser at National Taiwan Normal University’s physics department also looks promising:

An alternative, offering sequential playing of different frequencies will be needed for subsequent work; a purpose made interface for preference, though it could be done using a mathematics package or even BASIC at a pinch. Ivor has written one as a Java Applet, but security measures in the browser environment where it will be used are raising barriers which have still to be resolved.

More as the idea progresses…

[contributed by Ivor McGillivray and Felix Grant]

InspireDaisies

I have a standard data collection activity, borrowed from AbsentCat, which I call “Pushing up the daisies”. That’s not a very good name, bearing no relation to what actually happens, but it has the virtue of amusing pupils.It’s a quadrat exercise. Each pupil takes a pen, an old sock rolled into a ball, and a sheet of A4 card with a 100mm square hole in the centre of it. We all go to the centre of a convenient expanse of grass, form a circle facing outward, and throw our socks. Where the sock lands, put your sheet of card and count how many daisies are visible through the hole. Write the number down on the sheet of card, throw your sock again. Repeat until the novelty wears off, then return to the centre of the grass area to collate the results.

Sometimes, with a small group, I will replace both card and sock with a frisbee in the centre of which a circular 113mm hole (to match the area of the 100mm square) has been cut.Throwing things around in the open air is always preferable, on a sunny day, to being indoors. We usually take a picnic along, and a set of palmtop computers, so we can conduct the subsequent analysis of our daisy data in relaxation amongst the daisies themselves. This approach pays dividends: I get a lot of good natured work out of children who would get bored and impatient if we did academically equivalent work indoors.

This week, instead of the palmtops, my year fours (age 8-9) took a laptop with InspireData (reviewed here). Instead of writing their results on the card, and collating them later in a spreadsheet, the pupils brought each count back to the laptop and typed it into InspireData’s data entry “questionnaire”. Each observation was identified by the child’s name, and a photograph of a daisy was imported to replace the standard marker, so as the session proceeded we watched a growing histogram of labeled daisies gradually assemble on screen.

The class kept on gathering data much longer than usual, keen to see their name on screen as often as possible. Result: a much larger results database than usual, and more pupil involvement in the analysis phase.

I plan to follow up, at the end of this week, with botany and geography lessons based on the results using the InspireData histogram as a reference point for analogy with quantitative methods in both of those fields.

“Pushing up the daisies” is a good educational activity, offering a number of painless entry points to maths and science topics. InspireData adds immeasurably to it.

[contributed by Sayid]

InspireData (review)

Inspiration, the mind mapping software, is widely used in education. InspireData is a new addition, in this academic year, from the same publisher.The principle behind InspireData is much the same as its established sibling: visual learning by direct manipulation through an intuitive interface. I’ve never seen anything to compare with it: data are entered (or copied and pasted) into a conventional looking worksheet, instantly familiar to an Excel user, but nothing after that resembles what you may be used to in a spreadsheet, graphics program, or other data manipulation package. In trials with pupils and students aged from eight to eighty three, over the past few weeks, I’ve found it uniquely effective.

When you first switch from the worksheet to visualisation, you will find your data points scattered randomly all over the desktop. I found that this works well with introductory sorting exercises with found objects or record cards - especially if you start by applying a Venn diagram.

I say “applying” a Venn diagram, not “drawing” one, deliberately. Everything you (or the student) do here assembles itself before your eyes, each data point moving across the screen from its random initial position to the appropriate place in the graphic. Click the on screen Venn diagram button twice, to create two set loops; click each loop in turn and define them as “male” or “female”. Assuming that you have entered the name and gender of each pupil as your data, the points will travel quickly (but not too quickly) across the screen and cluster in the appropriate loop segments. Now switch on data point labels with another click, choosing “name”, and each point will show which pupil it represents. Now each member of the class can watch her or his own personal avatar move about in subsequent work.

Now click the stack diagram button. The Venn loops disappear, the points move again, and when everything comes to rest your pupils are stacked up in two bars above “male” and “female” markers, graphically showing the gender balance of the class.

Everything works the same way. If you entered the heights of your class members in centimetres, along with their genders, click the variable used for that stack chart and select “height”. More visual rearrangement, as the names shift around to align with the height bands which appear across the x-axis to replace the gender labels, for a schematic histogram. Select colouring, and the point beside each name changes hue to reflect gender - blue for girls, red for boys, perhaps. The way height is distributed by gender is immediately there for discussion. You can, if you wish, take the colouring back into a Venn diagram but this time define the loops as (for example) “height more than 120cm” and “height less than 150cm”, then discuss the way genders divide across the three set segments.

Pie charts work the same way. Leave the gender colouring in place, and define the sectors of the pie to reflect height bands - maybe start with the same three, then add more to increase the resolution as discussion develops. With each change, the names will shuffle about the screen to adopt their correct positions.

This needn’t seem to have anything to do with maths, so it’s a wonderful way to painlessly develop categorisation and quantitative vision alongside science as fun - possibly in an apparently nonscience context. I spent a session with a ten year old soccer team, feeding in their own choice of vital statistics for their personal heroes (club, field position, age, height, weight, number of goals last season…; for Beckham, Gerard, Rooney…).

Though I didn’t use it here, there is the facility to use custom icons (either across a whole variable or case by case), so a small photograph of each player would have been a valuable addition. Discussing the patterns which InspireData threw up, they generated their own questions, hypotheses, lines of enquiry. One of them had read a rule of thumb for ideal relation of height to weight - and InspireData moved the players (colour coded by performance) into a scattergram. Then, two hours in, one lad said: “could we use this for maths?”Getting the information into the worksheet is simplicity itself. There is a simple data entry form, called “Questionnaire”, into which each student can individually type their chosen information without having to navigate the worksheet at all. You can, if you wish, add helpful comments to each field (such as “how many goals did your player score last season?”). The user types into clearly laid out boxes, edits until they are happy, then a click commits the result to a row in the sheet.

For its purpose, and its level, I can’t praise this program highly enough. If you do any kind of data handling, in any subject, at any level where your learners are new to data analysis and would benefit from a visual approach, buy it.

[contributed by Felix Grant]